The Rangers exchanged arbitration figures with David Murphy on Friday and the two sides are about $1.5 million apart.
The Rangers offered $5.05 million, and Murphy, Texas' only arbitration-eligible player that remains unsigned, asked for $6.5 million.
General manager Jon Daniels earlier had expressed confidence that a deal will get done to avoid a hearing. The Rangers have not had an arbitration case advance to a hearing since Lee Stevens in 2000.
Murphy hit .304 with 15 home runs and 61 RBIs in 147 games last season and made $3.625 million.